The present invention relates to a control system for a magnetic bearing which utilizes magnetic attractive force of an electromagnet, and operates to support a moving member at high speed with high accuracy while magnetically positioning the moving member.
The magnetic bearing utilizing magnetically attractive force of an electromagnet is classified as an unstable system in view of control theory. Namely, it has a pole on the real axis of the right half area of the complex coordinate system. This unstability can be well understood according the following physical phenomenon occurring in the magnetic bearing. If a closed loop control device were not provided for the magnetic bearing, the electromagnet would fix the moving member under excessive magnetically attractive force or it would release away the moving member under too weak an attractive force.
Consequently, a compensator is needed to stabilize the magnetic bearing. The compensator can operate to stabilize the entire system of the magnetic bearing structure and to satisfy robustness thereof. However, a complicated adjusting work is needed to satisfy both of the stability of magnetic supporting and the robustness, i.e., performance to suppress disturbance with sufficient allowance. Under such circumstance, it would be quite difficult to add command control to displace or position the moving member in response to a command input.
The above mentioned situation can be theoretically explained as follows. With reference to Report of Japanese Mechanic Society, "Research of control system for a magnetic bearing of the thrust type", Vol. 255, 1967, provided that gravity m is applied to a magnetically supported member and electromagnetic attractive force F is applied to the member in the opposite direction, the kinetic equation for the supported member in the direction of Z is represented as follows: ##EQU1## Since mg=F(Z.sub.0, I.sub.0) is established in an equilibrium point, the relation (1) is expanded in terms of small displacements z and i as follows: ##EQU2## where .beta.=2 g/Z.sub.0, Km=Z.sub.0 /2 (I.sub.0 +I.sub.A),
F=K.sub.F (I+I.sub.A)/Z.sup.2 and I.sub.A : remanence compensation.
When the state variable is represented by x=[Z, Z].sup.T, the state equation is represented as follow: ##EQU3##
Consequently, the transfer function P(s) of the control object is represented as follow: ##EQU4##
It is understood from the transfer function (4) that the magnetic bearing is an unstable system having a pole at s=.sqroot..beta. on the real axis of the right half of the complex coordinate plane.
Next, FIG. 2 shows the conventional closed loop control device for the magnetic bearing. Displacement of the supported member is detected by a displacement detector 1. A detection signal therefrom is fed to an integral compensator 2 for improving the standing performance. Then, a phase advancing compensator 3 carries out processing of the signal in order to hold the pole s=.sqroot..beta. of the unstable control object to a stable side. Lastly, an electric power amplifier 4 is driven to magnetically activate an electromagnet so as to control the control object 15 such that the controller supported object is held in a gap space in place.
Sensitivity S(s) and complementary sensitivity T(s) are introduced to indicate performance characteristics of the closed loop system as follows: ##EQU5##
The relation (5) is known to indicate the stability and the robustness. FIG. 3 shows one example of the performance characteristics. In order to balance between the stability and the robustness, it is desired to adjust a crossover frequency without changing forms of S(j.omega.)and T(j.omega.). However, as is apparent from close evaluation of the relation (5), there is no parameter of the compensator effective to adjust only the crossover frequency. Adjustment of any compensator parameter would cause change of the forms of S(j.omega.) and T(j.omega.) as well as the crossover frequency therebetween. Stated otherwise, in order to balance between the stability and the robustness, various parameters of the compensator must be adjusted concurrently. Under such a situation, it is quite difficult to establish a certain level of responsiveness to a command input to displace the supported member according to the command input.
In the prior art, a considerable amount of time is needed to balance between the stability and the robustness in the entire system due to its complicated work. Therefore, although the conventional system can establish a magnetic bearing condition stably in actual running if it has the drawback that the responsiveness to command which can not be realized to a certain level at the same time.